<u>Given</u>:
Given that the two sides of the triangle are x, 4.0 and 5.6
We need to determine the range of possible sizes for the side x.
<u>Range of x:</u>
The range of x can be determined using the triangle inequality theorem.
The triangle inequality theorem states that, "if any side of a triangle must be shorter than the other two sides added together".
Thus, applying the theorem, we have;
![x=4.0+5.6](https://tex.z-dn.net/?f=x%3D4.0%2B5.6)
![x=9.6](https://tex.z-dn.net/?f=x%3D9.6)
Also, the the triangle inequality theorem states that, "the third side must be also larger than the difference between the other two sides".
Thus, we have;
![x=5.6-4.0](https://tex.z-dn.net/?f=x%3D5.6-4.0)
![x=1.6](https://tex.z-dn.net/?f=x%3D1.6)
Thus, the range of possible values for x are ![1.6](https://tex.z-dn.net/?f=1.6%3Cx%3C9.6)
Zero point six three two
numbers those are under 0. don't have values.
Your answer would be the bottom right image. In the bottom right image, x is divided by 5 consistently. No function can be determined in the other tables.
Answer:
![Leg\ 1 = 8](https://tex.z-dn.net/?f=Leg%5C%201%20%3D%208)
![Leg\ 2 = 15](https://tex.z-dn.net/?f=Leg%5C%202%20%3D%2015)
Step-by-step explanation:
Given: See Attachment
Required
Determine the length of the legs
To do this, we apply Pythagoras theorem.
![Hyp^2 = Adj^2 + Opp^2](https://tex.z-dn.net/?f=Hyp%5E2%20%3D%20Adj%5E2%20%2B%20Opp%5E2)
In this case:
![17^2 = x^2 + (2x- 1)^2](https://tex.z-dn.net/?f=17%5E2%20%3D%20x%5E2%20%2B%20%282x-%201%29%5E2)
Open Bracket
![17^2 = x^2 + 4x^2- 2x-2x + 1](https://tex.z-dn.net/?f=17%5E2%20%3D%20x%5E2%20%2B%204x%5E2-%202x-2x%20%2B%201)
![17^2 = 5x^2 - 4x + 1](https://tex.z-dn.net/?f=17%5E2%20%3D%205x%5E2%20-%204x%20%2B%201)
![289= 5x^2 - 4x + 1](https://tex.z-dn.net/?f=289%3D%205x%5E2%20-%204x%20%2B%201)
Collect Like Terms
![5x^2 - 4x + 1 - 289 = 0](https://tex.z-dn.net/?f=5x%5E2%20-%204x%20%2B%201%20-%20289%20%3D%200)
![5x^2 - 4x - 288 = 0](https://tex.z-dn.net/?f=5x%5E2%20-%204x%20-%20288%20%3D%200)
Solving using quadratic formula:
![x = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-b%5C%C2%B1%5Csqrt%7Bb%5E2%20-%204ac%7D%7D%7B2a%7D)
So:
or ![x = -7.2](https://tex.z-dn.net/?f=x%20%3D%20-7.2)
Since, x can't be negative, then:
![x = 8](https://tex.z-dn.net/?f=x%20%3D%208)
One of the leg is:
![Leg\ 1 = x](https://tex.z-dn.net/?f=Leg%5C%201%20%3D%20x)
![Leg\ 1 = 8](https://tex.z-dn.net/?f=Leg%5C%201%20%3D%208)
![Leg\ 2 = 2x - 1](https://tex.z-dn.net/?f=Leg%5C%202%20%3D%202x%20-%201)
![Leg\ 2 = 2*8 - 1](https://tex.z-dn.net/?f=Leg%5C%202%20%3D%202%2A8%20-%201)
![Leg\ 2 = 16 - 1](https://tex.z-dn.net/?f=Leg%5C%202%20%3D%2016%20-%201)
![Leg\ 2 = 15](https://tex.z-dn.net/?f=Leg%5C%202%20%3D%2015)
Rewrite in slope intercept from y=mx+b y=1-3x+11/3